function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

z = X * theta;
h = 1 ./ (1 .+ exp(0 .- z))
J = (y' * log(h) + (1 .- y)' * log(1 .- h)) ./ (0 - m) + sum (theta(2:size(theta)) .^ 2) * lambda / (2 * m)

extra = lambda * theta
extra(1) = 0

grad = (X' * (h - y) + extra) / m




% =============================================================

end
